The X Air Conditioning Company is considering purchase of a special shipment of

Question

The X Air Conditioning Company is considering purchase of a special shipment of portable air conditioners from Japan. Each unit will cost X $800 and be sold for $1250. X does not want to carry over surplus air conditioners to the following year. Thus, all supplies will be sold to a wholesaler, Paul & Company, who has agreed to take all surplus units for $500 per unit. The probability distribution for air conditioners is shown below:

Demand: 5, 6, 7, 8, 9

Estimated Probability: 0.3, 0.15, 0.25, 0.15, 0.15

(a) What are X’s optimal order quantity and the expected profit?

(b) If X has surplus then Paul & Company agreed to take all surpluses from X for $500 per unit plus a fixed charge of $200 (e.g., X’s pay Paul & Company $200 fixed charge & receive from Paul & Company the surplus times $500). What is the expected profit if X ordered 8 air conditioners from Japan?

Explanation / Answer

(a) Optimal order quantity = sum of all demands and respective probabilities

= 0.3*5 + 0.15*6 + 0.25*7 + 0.15*8 + 0.15*9 = 1.5 + 0.9 + 1.75 + 1.2 + 1.35 = 6.7 7...optimal order quantity

expected profit (we calculate for 10 periods, since order qty is in decimal) i.e. 67 units will be sold when 70 ordered

profit = 67 * 450 - 3* 300 = $29,250, so for a year, profit = $ 2,925......(450 is profit per unit, 300 is loss when surplus is returned at $500)

(b) For 8 air conditioners ordered : (Again lets calculate for 10 periods)

profit = 67* 450 - 13* 300 - 200 = $26,050.......(200 is one time fixed cost)

so, profit for 1 year in case of 8 air conditioners purchased = $ 2,605

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